Monday, July 27, 2015

a physical feeling for densities

who: J1
when: after lunch
where: our stairs

Thanks to Mom, our stair number line recently got a (partial) refresh with some snazzy new number posters. This stimulated a new exploration by J1 to study how dense different groups of numbers are. Well, that wasn't how he phrased it . . .

J1's dialogue as he played on the stairs:
Hmm, what if I walk up the multiples of 2? <walks up skipping stairs, no problem here>
Oh, that's pretty easy, but J3 might find it tricky.

What about squares? 1, 4, what's next ...?
Ooh, 9, that's hard. <finds a cheat by wedging his feet against the sides of the stairs so that he isn't touching the stairs in between>
What's next? 16, oh no! <seeing that it is too far to get by himself>

What about primes?
2 <easy>
3 <very easy>
5, 7 <not to bad>
9? No!
11... daddy, please help! <I help lever him up onto 11>
13, easy!
15, no... 17 <slips as he tries a couple of tricks to get to the 17th step>

Okay, now let's try multiples of 4

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